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If y = |2 + x| - |2 – x| and |2x – 15| < 2, how many integer values can y take?
- a)1
- b)0
- c)2
- d)4
- e)Cannot be determined
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If y = |2 + x| - |2 – x| and |2x – 15| < 2, how many in...
Solving |2x – 15| < 2 first to get range of x
(2x – 15) < 2
x < 8.5
-(2x – 15) < 2
x > 6.5
Range of x 6.5 < x < 8.5
y = |2 + x| - |2 – x| to see that there is only 1 solution.
|2 + x| = 2 + x ...... is always +ve , x > 2 as (6.5 < x < 8.5)
|2 – x| = −(2 − x) ...... range of x > 2 , so 2 - x will be negative
y = |2 + x| − |2 – x|
y = 2 + x − (−(2−x))
y = 4;
(2x – 15) < 2
x < 8.5
-(2x – 15) < 2
x > 6.5
Range of x 6.5 < x < 8.5
y = |2 + x| - |2 – x| to see that there is only 1 solution.
|2 + x| = 2 + x ...... is always +ve , x > 2 as (6.5 < x < 8.5)
|2 – x| = −(2 − x) ...... range of x > 2 , so 2 - x will be negative
y = |2 + x| − |2 – x|
y = 2 + x − (−(2−x))
y = 4;
constant value
Most Upvoted Answer
If y = |2 + x| - |2 – x| and |2x – 15| < 2, how many in...
Given Information:
The given equations are:
1. y = |2 + x| - |2 - x|
2. |2x - 15| < />
Solution:
Analysis of Equation 1:
The expression y = |2 + x| - |2 - x| can be simplified as follows:
When x ≥ -2,
y = (2 + x) - (2 - x) = 2 + x - 2 + x = 2x
When x < />
y = -(2 + x) - (2 - x) = -2 - x - 2 + x = -4
So, the possible values of y are 2x and -4.
Analysis of Equation 2:
|2x - 15| < />
-2 < 2x="" -="" 15="" />< />
13 < 2x="" />< />
6.5 < x="" />< />
The possible integer values for x are 7 and 8.
Combining the Results:
When x = 7, y = 2(7) = 14
When x = 8, y = 2(8) = 16
Therefore, the only possible integer values for y are 14 and 16. Hence, the correct answer is option 'A', which is 0 integer values for y.
The given equations are:
1. y = |2 + x| - |2 - x|
2. |2x - 15| < />
Solution:
Analysis of Equation 1:
The expression y = |2 + x| - |2 - x| can be simplified as follows:
When x ≥ -2,
y = (2 + x) - (2 - x) = 2 + x - 2 + x = 2x
When x < />
y = -(2 + x) - (2 - x) = -2 - x - 2 + x = -4
So, the possible values of y are 2x and -4.
Analysis of Equation 2:
|2x - 15| < />
-2 < 2x="" -="" 15="" />< />
13 < 2x="" />< />
6.5 < x="" />< />
The possible integer values for x are 7 and 8.
Combining the Results:
When x = 7, y = 2(7) = 14
When x = 8, y = 2(8) = 16
Therefore, the only possible integer values for y are 14 and 16. Hence, the correct answer is option 'A', which is 0 integer values for y.
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If y = |2 + x| - |2 – x| and |2x – 15| < 2, how many integer values can y take?a)1b)0c)2d)4e)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If y = |2 + x| - |2 – x| and |2x – 15| < 2, how many integer values can y take?a)1b)0c)2d)4e)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y = |2 + x| - |2 – x| and |2x – 15| < 2, how many integer values can y take?a)1b)0c)2d)4e)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?.
If y = |2 + x| - |2 – x| and |2x – 15| < 2, how many integer values can y take?a)1b)0c)2d)4e)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If y = |2 + x| - |2 – x| and |2x – 15| < 2, how many integer values can y take?a)1b)0c)2d)4e)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y = |2 + x| - |2 – x| and |2x – 15| < 2, how many integer values can y take?a)1b)0c)2d)4e)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?.
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